Big Ideas Math Algebra 1, 2015
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Big Ideas Math Algebra 1, 2015 View details
1. Graphing Square Root Functions
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Exercise 1 Page 548

Functions are named based on which algebraic expressions they contain.

radical function

Practice makes perfect

We are asked to complete the given sentence.

A is a function that contains a radical expression with the independent variable in the radicand.

Functions can contain many types of algebraic expressions and can be named based on which expressions they contain. Let's take a look at some of the different types of functions and which expressions they contain.

Name of the Function Example Characteristic of the Function
Linear Function The highest exponent of the independent variable is
Quadratic Function The highest exponent of the independent variable is
Cubic Function The highest exponent of the independent variable is
Exponential Function The function contains a variable exponent.
Absolute Value Function The function contains the absolute value of a variable expression.
Square Root Function The function contains a radical expression with an index of and the independent variable in the radicand.
Cube Root Function The function contains a radical expression with an index of and the independent variable in the radicand.

Notice that both the square root function and the cube root function contain radical expressions with the independent variable in the radicand. Since the common characteristic between them is that they include variable expressions under a radical sign, they are also known as radical functions. Knowing this, we can complete our sentence.

A radical function is a function that contains a radical expression with the independent variable in the radicand.